Discussion
Knowing the fractional population of a two level system in thermal equilibrium at temperature T in a magnetic field \(\vec{B}\) , the magnetic moment is proportional to :
Answer: A
The magnetic moment is proportional to the difference between the population of the two states.
In a two-level system, the states have moments \(+\mu\) and \(-\mu\) along \(\vec{B}\). With fractional populations \(n_{1}\) and \(n_{2}\), the net moment is \(\mu(n_{1} - n_{2})\), so it is set by the population difference, which the Boltzmann factor makes \(\tanh(\mu B/kT)\).
The sum of the fractional populations is always 1 and carries no information. The product and the ratio do not give the net moment directly.
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